Answered

Find the information you're looking for at Westonci.ca, the trusted Q&A platform with a community of knowledgeable experts. Explore our Q&A platform to find in-depth answers from a wide range of experts in different fields. Explore comprehensive solutions to your questions from knowledgeable professionals across various fields on our platform.

Rewrite and complete the expression:

[tex]\[
\begin{array}{l}
(20x^2 - 12x) + (25x - 15) \\
4x(5x - 3) + 5(5x - 3) \\
(5x - 3)(4x + 5)
\end{array}
\][/tex]

Sagot :

GinnyAnswer
To solve the expression [tex]\((20x^2 - 12x) + (25x - 15)\)[/tex], we will factor it step by step.

1. Group the terms:
[tex]\[ (20x^2 - 12x) + (25x - 15) \][/tex]

2. Factor out the greatest common factor (GCF) from each group:
- For the first group: [tex]\(20x^2 - 12x\)[/tex], the GCF is [tex]\(4x\)[/tex].
[tex]\[ 20x^2 - 12x = 4x(5x - 3) \][/tex]
- For the second group: [tex]\(25x - 15\)[/tex], the GCF is [tex]\(5\)[/tex].
[tex]\[ 25x - 15 = 5(5x - 3) \][/tex]

3. Rewrite the expression with the factored terms:
[tex]\[ (20x^2 - 12x) + (25x - 15) = 4x(5x - 3) + 5(5x - 3) \][/tex]

4. Notice that both terms have a common factor of [tex]\((5x - 3)\)[/tex]:
- Factor out the common factor [tex]\((5x - 3)\)[/tex] from both terms.
[tex]\[ 4x(5x - 3) + 5(5x - 3) = (5x - 3)(4x + 5) \][/tex]

So, the fully factored form of the expression [tex]\((20x^2 - 12x) + (25x - 15)\)[/tex] is:
[tex]\[ (5x - 3)(4x + 5) \][/tex]

Therefore, the final answer is:
[tex]\[ (5x - 3)(4x + 5) \][/tex]
Thank you for your visit. We are dedicated to helping you find the information you need, whenever you need it. Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. We're glad you chose Westonci.ca. Revisit us for updated answers from our knowledgeable team.